Riemann sums question

1. Jan 15, 2005

KataKoniK

When calculating Lf(P) and Uf(P) there can be many different answers correct? Provided that you solved it properly.

2. Jan 15, 2005

dextercioby

What do you mean??Have you read you question after writing it,to see whether it makes any sense?If the superior Riemann sum is different from the inferior one,the definite integral does not exist.Period.Since they involve taking a limit,that is not multivalued.

Daniel.

3. Jan 15, 2005

HallsofIvy

Staff Emeritus
That's not a very well phrased question. If you are given a particular partition, P, and a function, f, the Lf(P) is the sum of "length of interval times least value of f in that interval" and is a specific number. There are not "many different answers". The same is true of Uf(P). In general, Lf(P)< Uf(P).

Of course, a different choice of P might result in different answers.

4. Jan 15, 2005

KataKoniK

Thanks for the replies. I was just looking over some examples. So, just say they give a P = {0, 2, 3, 4} etc. they say to choose a number in between for ie. 0 and 2, so 1/2 or 1/4 would be correct choices, which will also result in a diff ans if one chose 1/2 instead of 1/4. I'm just learning this stuff, so sorry if I wasn't clear enough.

5. Jan 15, 2005

nm I got it!